CIMPA-ICTP RESEARCH SCHOOL on ALGEBRAIC CURVES OVER FINITE FIELDS 2013 Manila, Philippines, 22 July - 2 August 2013.

The CIMPA-ICTP Research School on Algebraic Curves over Finite Fields and Applications was held in Manila, Philippines, bringing together 67 mathematicians and graduate students from 15 countries (including 10 lecturers) in a two-week workshop consisting of lectures/discussions and computation sessions on algebraic curves.

The theory of algebraic curves over finite fields is a very active subject both from a theoretical and an applied point of view. The research school covered theoretical, computational and applied aspects of the topic and thus is useful to a broad range of students and young mathematicians interested in algebra and its applications.

The CIMPA-ICTP research school developed the subject almost from scratch, beginning from introductory classes on finite fields and algebraic curves. We covered aspects of the theory of elliptic curves over finite fields as well as the application of the Riemann-Roch theorem to the zeta function of an algebraic curve over a finite field (including the Stepanov- Bombieri-Schmidt proof of the Riemann hypothesis). Applications also figured prominently with sessions on elliptic curve cryptography, coding theory and computational examples using Pari GP and Sage. Moreover we covered the explicit construction of elliptic curves over finite fields with group of points of large prime order (as needed by cryptographic applications) via complex multiplication.

All lectures and discussions were conducted in English.

The School was held at the Institute of Mathematics, University of the Philippines, Diliman, Quezon City, Philippines.